Binomial Theorem

Some particular expansions for Fractional Index

For n

Q, we have:

Example:

Write the first four terms in the ascending powers of x in the expansions of the following:

Suggested answer:

|4x|=|4||x|

= 4|x|<4(1/4)=1.

|4x|<1

(1 + 4x)^-⁵ can be expanded by Binomial theorem.

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	Introduction
	Principle of Mathematical Induction
	Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method)
	Method of writing expansion
	Some particular expansions for Positive Integral Index
	General Term for Positive Integral Index
	Middle Terms for Positive Integral Index
	Particular Terms for Positive Integral Index
	Greatest Terms for Positive Integral Index
	Some Applications of Binomial Theorem for Positive Integral Index
	Binomial Theorem for Fractional Index
	Some particular expansions for Fractional Index
	General Term for Fractional Index
	Particular Terms for Fractional Index
	Some Applications of Binomial Theorem for Fractional Index
	Summary

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English
Math
Geometry